TOTAL ODDS AND OTHER OBJECTIVES FOR CLUSTERING VIA MULTINOMIAL-LOGIT MODEL
Stan Lipovetsky · Advances in Adaptive Data Analysis · 2012
This work considers maximum likelihood objectives for estimating the probability of each multivariate observation's assignment to one particular cluster or to one or more clusters. Combining both objectives yields a maximization of the total probability odds of belonging to one or another cluster. The gradient of the total odds objective can be reduced to the multinomial-logit probabilities leading to a convenient Newton–Raphson clustering procedure presented via an iteratively re-weighted least squares technique. Besides the total odds, several other new objectives are also considered, and numerical examples are discussed.